Cementing, as a common operation in well drilling and completions, requires accurate calculations and feasible studies. High-quality well cementing is necessary to achieve objectives and to prevent accidents and damage. The correct levels of cementation and cementation of good quality must be achieved, and thus both of these must be accurately evaluated. Cement bond quality can be assessed in various methods, for instance, the use of acoustic equipment. Acoustic readings can be processed to generate graphics of the cement status. These images are inspected by experts who assess the cement bonding visually, providing qualitative estimates of their quality. Regarding the explanations, industry needs automatic, fast, and intelligent methods. In this study, the performance of neural networks for automatic interpretation was evaluated and combined with fuzzy systems. We present a convolutional neural network (CNN) to address these challenges. The data were extracted from the oilwell logs of District 1 of Ahvaz, sampled by the National Iranian South Oil Company (NISOC), and were divided into three classes of cementing bond quality—namely, good, midrate, and bad. Each class contained 1 m data entries. The input to the CNN comprised images of sampled variable density logs (VDLs). In the second stage of analysis, the weights of the learned networks were optimized and replaced with a Bees algorithm (BA) and a fuzzy system (fuzzy-CNN). The estimated efficiency of the CNN to classify the well cement quality and fuzzy-CNN was 80.15 and 83.62%, respectively. The study provides insight into the efficiency and outputs of each of the networks studied. Problems encountered in training the networks to operate optimally as an automatic interpretation system were investigated and are discussed.